I would agree with laktronics, do not attempt this with only a three pin serial port. There are self powered converters on the market and they work fine. However, they rely on using the optional RS232 control pins as power sources. Specifically, RTS and DTR. To use these converters, the PC software must set RTS and DTR to the appropriate level and keep them there. If the OS or some other software accesses that serial port and changes these control lines, the converter becomes unpowered and communication fails.
A simple and more bullet proof solution is to get your power elsewhere. The USB port has a dedicated +5V power source for external devices. I would suggest buying a USB to RS232 converter. Open it up and connect into the +5V supply to get power for your MAX232 and your RS422 transceiver. Then everyone is happy. The ICs get a dedicated power source that is stable and the OS sees a serial port with all the proper mappings and no special control pin setups.
----- Steve